Question: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = -6$ $a_i = a_{i-1} - 4$ What is $a_{4}$, the fourth term in the sequence?
Explanation: From the given formula, we can see that the first term of the sequence is $-6$ and the common difference is $-4$ To find the fourth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = -6 - 4(i - 1)$ To find $a_{4}$ , we can simply substitute $i = 4$ into the our formula. Therefore, the fourth term is equal to $a_{4} = -6 - 4 (4 - 1) = -18$.